Flutter and long-wave instabilities in compliant channels conveying developing flows

1997 ◽  
Vol 331 ◽  
pp. 37-58 ◽  
Author(s):  
P. G. LAROSE ◽  
J. B. GROTBERG
Keyword(s):  
Flow Speed ◽  
Infinite Length ◽  
Wave Instability ◽  
Flutter Instability ◽  
Long Wave ◽  
Developing Flow ◽  
Theoretical Predictions ◽  
Parameter Values ◽  
Correction Terms ◽  
Special Parameter

A partially collapsed lung airway or other flexible tube is modelled as a two-dimensional channel of infinite length. We consider the linear stability of this system conveying a developing flow, analysing the full Orr–Sommerfeld system analytically for long waves and numerically for arbitrary wavelengths. We find a long-wave instability which has not been observed in previous channel studies. This long-wave instability is stabilized by increasing the elastance of the wall, but other wall properties do not affect it except in correction terms. In addition to the long-wave instability, there is the finite wavelength (flutter) instability, which, depending on the parameter values chosen, may be critical at a higher or lower flow speed than the long-wave instability. For special parameter values the long-wave and flutter instabilities are critical at the same flow speed. Comparisons with experiments show that theoretical predictions are in agreement with experimental observations.

Side-Wall Effect on the Long-Wave Instability in Kolmogorov Flow

1998 ◽  
Vol 67 (5) ◽  
pp. 1597-1602 ◽  
Author(s):  
Hiroaki Fukuta ◽  
Youichi Murakami
Keyword(s):  
Side Wall ◽  
Wall Effect ◽  
Wave Instability ◽  
Kolmogorov Flow ◽  
Long Wave

Negative energy standing wave instability in the presence of flow

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Michael S. Ruderman
Keyword(s):  
Standing Wave ◽  
Negative Energy ◽  
Flow Speed ◽  
Tangential Discontinuity ◽  
Positive Energy ◽  
Wave Instability ◽  
Long Wavelength ◽  
Backward Wave ◽  
Moving Plasma ◽  
The Difference

We study standing waves on the surface of a tangential discontinuity in an incompressible plasma. The plasma is moving with constant velocity at one side of the discontinuity, while it is at rest at the other side. The moving plasma is ideal and the plasma at rest is viscous. We only consider the long wavelength limit where the viscous Reynolds number is large. A standing wave is a superposition of a forward and a backward wave. When the flow speed is between the critical speed and the Kelvin–Helmholtz threshold the backward wave is a negative energy wave, while the forward wave is always a positive energy wave. We show that viscosity causes the standing wave to grow. Its increment is equal to the difference between the negative energy wave increment and the positive energy wave decrement.

scholarly journals Anticipating the emergence of infectious diseases

2017 ◽  
Vol 14 (132) ◽  
pp. 20170115 ◽  
Author(s):  
Tobias S. Brett ◽  
John M. Drake ◽  
Pejman Rohani
Keyword(s):  
Large Scale ◽  
Simulated Data ◽  
Disease Emergence ◽  
General Applicability ◽  
Slowing Down ◽  
Animal Populations ◽  
Theoretical Predictions ◽  
Parameter Values ◽  
Model Structures ◽  
Good Support

In spite of medical breakthroughs, the emergence of pathogens continues to pose threats to both human and animal populations. We present candidate approaches for anticipating disease emergence prior to large-scale outbreaks. Through use of ideas from the theories of dynamical systems and stochastic processes we develop approaches which are not specific to a particular disease system or model, but instead have general applicability. The indicators of disease emergence detailed in this paper can be classified into two parallel approaches: a set of early-warning signals based around the theory of critical slowing down and a likelihood-based approach. To test the reliability of these two approaches we contrast theoretical predictions with simulated data. We find good support for our methods across a range of different model structures and parameter values.

scholarly journals Formation of Kinneyia via shear-induced instabilities in microbial mats

2013 ◽  
Vol 371 (2004) ◽  
pp. 20120362 ◽  
Author(s):  
Katherine Thomas ◽  
Stephan Herminghaus ◽  
Hubertus Porada ◽  
Lucas Goehring
Keyword(s):  
Microbial Mats ◽  
Flow Speed ◽  
Glass Beads ◽  
Flowing Water ◽  
Flow Conditions ◽  
Theoretical Predictions ◽  
Laboratory Analogue ◽  
Littoral Habitats ◽  
Over Time ◽  
Ripple Pattern

Kinneyia are a class of microbially mediated sedimentary fossils. Characterized by clearly defined ripple structures, Kinneyia are generally found in areas that were formally littoral habitats and covered by microbial mats. To date, there has been no conclusive explanation of the processes involved in the formation of these fossils. Microbial mats behave like viscoelastic fluids. We propose that the key mechanism involved in the formation of Kinneyia is a Kelvin–Helmholtz-type instability induced in a viscoelastic film under flowing water. A ripple corrugation is spontaneously induced in the film and grows in amplitude over time. Theoretical predictions show that the ripple instability has a wavelength proportional to the thickness of the film. Experiments carried out using viscoelastic films confirm this prediction. The ripple pattern that forms has a wavelength roughly three times the thickness of the film. This behaviour is independent of the viscosity of the film and the flow conditions. Laboratory-analogue Kinneyia were formed via the sedimentation of glass beads, which preferentially deposit in the troughs of the ripples. Well-ordered patterns form, with both honeycomb-like and parallel ridges being observed, depending on the flow speed. These patterns correspond well with those found in Kinneyia, with similar morphologies, wavelengths and amplitudes being observed.

The mechanism for the long-wave instability in thin liquid films

1990 ◽  
Vol 217 ◽  
pp. 469-485 ◽  
Author(s):  
Marc K. Smith
Keyword(s):  
Physical Mechanism ◽  
Thin Liquid Film ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
The Other ◽  
Wave Instability ◽  
Inclined Plane ◽  
Long Wave ◽  
The Many ◽  
Large Groups

A physical mechanism for the long-wave instability of thin liquid films is presented. We show that the many diverse systems that exhibit this instability can be classified into two large groups. Each group is studied using the model of a thin liquid film with a deformable top surface flowing down a rigid inclined plane. In the first group, the top surface has an imposed stress, while in the other, an imposed velocity. The proposed mechanism shows how the details of the energy transfer from the basic state to the disturbance are handled differently in each of these cases, and how a common growth mechanism produces the unstable motion of the disturbance.

Long-wave instability of a helical vortex

2015 ◽  
Vol 780 ◽  
pp. 687-716 ◽  
Author(s):  
Hugo Umberto Quaranta ◽  
Hadrien Bolnot ◽  
Thomas Leweke
Keyword(s):  
Growth Rate ◽  
Water Channel ◽  
Vortex Filament ◽  
Linear Stability Theory ◽  
Wave Instability ◽  
Characteristic Distance ◽  
Long Wave ◽  
Instability Modes ◽  
Small Pitch ◽  
Helical Vortex

We investigate the instability of a single helical vortex filament of small pitch with respect to displacement perturbations whose wavelength is large compared to the vortex core size. We first revisit previous theoretical analyses concerning infinite Rankine vortices, and consider in addition the more realistic case of vortices with Gausssian vorticity distributions and axial core flow. We show that the various instability modes are related to the local pairing of successive helix turns through mutual induction, and that the growth rate curve can be qualitatively and quantitatively predicted from the classical pairing of an array of point vortices. We then present results from an experimental study of a helical vortex filament generated in a water channel by a single-bladed rotor under carefully controlled conditions. Various modes of displacement perturbations could be triggered by suitable modulation of the blade rotation. Dye visualisations and particle image velocimetry allowed a detailed characterisation of the vortex geometry and the determination of the growth rate of the long-wave instability modes, showing good agreement with theoretical predictions for the experimental base flow. The long-term (downstream) development of the pairing instability leads to a grouping and swapping of helix loops. Despite the resulting complicated three-dimensional structure, the vortex filaments surprisingly remain mostly intact in our observation interval. The characteristic distance of evolution of the helical wake behind the rotor decreases with increasing initial amplitude of the perturbations; this can be predicted from the linear stability theory.

Dissipative effects on the resonant flow of a stratified fluid over topography

1988 ◽  
Vol 192 ◽  
pp. 287-312 ◽  
Author(s):  
N. F. Smyth
Keyword(s):  
Bottom Topography ◽  
Stratified Fluid ◽  
Flow Speed ◽  
Resonant Condition ◽  
Weakly Nonlinear ◽  
Dissipative Effects ◽  
Long Wave ◽  
Near Resonance ◽  
Wave Limit ◽  
Wave Modes

The effect of dissipation on the flow of a stratified fluid over topography is considered in the weakly nonlinear, long-wave limit for the case when the flow is near resonance, i.e. the basic flow speed is close to a linear long-wave speed for one of the long-wave modes. The two types of dissipation considered are the dissipation due to viscosity acting in boundary layers and/or interfaces and the dissipation due to viscosity acting in the fluid as a whole. The effect of changing bottom topography on the flow produced by a force moving at a resonant velocity is also considered. In this case, the resonant condition is that the force velocity is close to a linear long-wave velocity for one of the long-wave modes. It is found that in most cases, these extra effects result in the formation of a steady state, in contrast to the flow without these effects, which remains unsteady for all time. The flow resulting under the action of boundary-layer dissipation is compared with recent experimental results.

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